Question

A man consumes 3000 kcal of food in one day, converting most of it to thermal energy to maintain body temperature. If he loses half this energy by evaporating water (through breathing and sweating), how many kilograms of water evaporate?

(a) 0.375 kg
(b) 0.500 kg
(c) 0.625 kg
(d) 0.750 kg

Answer 1

The mass of water that evaporates is calculated using the enthalpy of vaporization at body temperature, resulting in 2.584 kg, which differs from the provided options, suggesting a possible error in the question or choices.

Step-by-step explanation:

When a man consumes 3000 kcal of food in a day and loses half of this energy through the evaporation of water, we need to calculate the mass of water evaporated. To find this, we use the enthalpy of vaporization of water at body temperature, which is approximately 2428 kJ/kg.

Since he loses half of the 3000 kcal consumed, this results in 1500 kcal, which converts to 6276 kJ (1 kcal = 4.184 kJ). The mass of water evaporated m is then calculated using the formula:

m = Total Energy Lost / Enthalpy of Vaporization

m = 6276 kJ / 2428 kJ/kg = 2.584 kg

However, this answer is not listed in the options provided. It is possible the question includes a typo, assumption, or omitted value leading to the incorrect set of answer choices.